Computing instrument.



J. l. WHITE.

COMPUTING INSTRUMENT.

APPLICATION FILED SE'PT.21. 1914.

Patented Dee. 7, 1915.

2 SHEETS*SHEET l.

@Moen/fo@ O 0V 0 m w COLUMBIA PLANoaRAPT-l co.,wAsHlNGToN, D. c.

I. I. WHITE.

COMPUTING INSTRUMENT.

APPucATIoN FILED sEPT.21.1914.

Patented Dec. 7, 1915.

2 SHEETS-SHEET 2.

314 @e1/dro@ Wmme@ cuLUAmlA 'PLANOGRAPM co., WASHINGTON. D. c.

UNITED STATES PATENT OFFICE.

JOHN J'. WHITE, 0F ARVADA, COLORADO, SSIGNOR OF ONE-FOURTH TO J'. A.PIERCE, OF ARVADA, COLORADO.

COMPUTING INSTRUMENT.

Specification of Letters Patent.

Patented Dec. '7, 1915.

To all whom t may concern Be it known that I, JOHN J. WHITE, a citizenof the United States, residing at Arvada, county of Jefferson, and Stateof Colorado, have invented certain new and useful Improvements inComputing Instruments; and I do declare the following to be a. full,clear, and exact description of the invention, such as will enableothers skilled in the art to which it appertains to make and use thesame, reference being had to the accompanying drawings, and to thecharacters of reference marked thereon, which form a part of thisspeciiication.

My invention relates to improvements in a computing device, and moreparticularlyto a device for computing the circumferences and areas ofcircles when the diameters are known.

4 The object of this invention is to produce a device of the characterstated whichy shall be simple in construction and easily operated, notrequiring a knowledge of mathematics. l y

Generally speaking, the device consists of a combination of disks and anindicator mounted in a circular casing and operating in connection witha train of gears in such a manner that the circumference or area of thecircle of any given diameter may be readily obtained, all of which willbe hereinafter more fully described and pointed out in the claims.

Having briefly outlined my improved construction, I will proceed todescribe the same 1n detail. reference being made to the accompanyingdrawing, in which is illustrated i an embodiment thereof. In thisdrawing,-

Figure 1 is a face view of my improved device, showing a table of areasof circles radially arranged from a given center. Fig. 2 is `a view ofthe opposite face of the device, showing the manipulating disks. Fig. 3is a vertical section taken on the line 3-3, Fig. 1, looking toward theleft. Fig. 4 is a section taken on the line 4-4, Fig. 3, looking towardthe left. Fig. 5 is a view taken on the line 5 5, Fig. 3, looking towardthe left.

The same reference characters indicate the same parts in all the views.

Let the numeral designate a metal ring provided with an annular flange 6formed on one edge thereof for retaining a transparent disk 7 preferablycomposed of glass.

and which is fitted into said ring, the outer edge of the glass engagingthe flange on the inside. Also fitted into the ring 5 is a casing Swhich consists of an inner or `bottom plate 9 having an annular liangeat its outer edge and projecting in a direction opposite the glass disk7. To the outer edge of this flange is secured a cover composed of aplate 10, the latter being held in place by suitable fastening devicesas screws 11. Yithin the casing 8 as thus defined are mounted gear ortoothed wheels 1Q, 18 and 1'1, on spindles 15, 1G and 17, respectively.The gear 12 has eight teeth and its spindle 15 protrudes through theplate 10 and a disk IS, which is mounted and made fast to its protrudingextremity. The opposite extremity of this spindle is journaled in thebottom or inner plate 9 of the casing. The gear 13 has thirty-two teethand its spindle 16 protrudes through the bottom or inner plate 9 of thecasing, and to this protruding extremity is secured an indicating arm orpointer 19. The gear 142 has seven teeth and its spindle 17 protrudesthrough the plate 10 and has a disk 20 mounted on and made fast to itsprotruding end. The opposite end of this spindle is journaled in theinner or bottom plate 9.

The outer portion of the disk 1S adjacent its periphery is divided byradial lines into eight equal sections. This disk will for convenience,be herein termed the traveling or manipulating disk. The disk 20 which Iwill term the fractional disk, is divided adjacentits periphery bysimilar radial lines, into sixteen equal sections.

On the inner face of the corresponding disk 9 is mounted a chart 21divided by radial lines, whereby sect-or shaped or partially sectorshaped spaces are formed in which the areas of circles are expressed bysuitable idicia as numerals; the circles whose areas are thus indicatedon this particular chart have diameters from four to twentyfour inches,inclusive. The chart is divided by circles or circular lines into liveZones, t-he aforesaid radial lines being employed to subdivide theinnermost zone into sixteen equal parts; the next outer Zone immediatelyadjacent the innermost zone being divided by the radial lines intothirty-two equal parts; and the remaining zones each into sixty-fourequal parts. In the innermost Vzone are printed or otherwise suitablyformed, the areas of circles'from four t o seven and three-fourthsinches in diameter, each` successive expression being the area of acircle whose diameter is 1/4 of an inch greater than the precedingexpression. That is to say, the diameters of the circles whose areas areexpressed in the innermost Zone are l inches; l 1 inches; el 1/2 inches;Ll; 3/1- inches, and so on. In the next zone, areas are formed ofcircles from eight to eleven and seven-eighths inches in diameter, eachsuccessive expression being the area of a circle whose diameter is 1/8of an inch greater than the preceding expression. That is t0 say, thediameter of the circles whose areas are expressed in the zone next tothe innermost zone are 8 inches; 8 1/8 inches; 8 2/8 inches; 8 3/8inches, and so on. In the next outer Zone are found areas of circlesfrom twelve to fifteen and fifteen-six- Vteenths inches in diameter,each successive expression being the area of a circle whose diameter is1/16 of an inch greater than the preceding expression. That is to say,the diameter of circles whose areas are ex` pressed in this rone are 12inches; 12 1/16 inches; 12 2/16 inches; 12 3/16 inches, and so on, andcontinuing in this order to the last zone, where the areas of circleshaving diameters from twenty-three to twenty-l three andfifteen-sixteenths inches, respectively, are given, each successiveexpression being the area cf a circle whose diameter is 1/16 of an inchGreaterlthan the preceding expression, as heretofore explained. The nextor final division of the fifth Zone, being the completion of the cycle,and corresponding to a circle whose diameter is twentyfour inches, hasits area printed in the center of the chart, as all ofthe other spaceshave been previously filled. The chart is further divided into quadrantsby heavy lines A, B, C and D, respectively, and the table printed ineach zone starts from the line A, reading toward the right.

In operation, the device is set with the indicator 19 parallel with theline A, its point being exposed through Vthe glass 7 at the outer edgeof the chart, the latter being of slightly less area than the exposedsurface of the disk (see Fig. 1) and with the traveling disk 18 and thefractional disk 20 in the position shown in Fig. 2. A small recess 22 isformed in the traveling disk 18 to receive a pointed instrument in orderto facilitate the manipulation of the disk and the operation of theinstrument for determining the circumferences and areas of circles.

To find the circumference of a circle of a given diameter, the travelingdisk is turned toward the left or in the direction indicated by thearrow in Fig. 2, as many revolutions as there are inches inthe diameterof the circle, and by virtue of the gear connection with the fractionaldisk 20, it will be seen that each revolution of the disk 18 will causethe disk 20 to travel one revolution and a fraction. The aggregate ofthis additional travel of the fractional disk during Ythe severalrevolutions of the traveling disk, added to three times the number ofrevolutions of the traveling disk, will give the circumference of thecircle. It will thus be seen that the gearing connection between thetraveling disk and the fractional disk is such that the additionaltravel of the fractional disk beyond the corresponding number ofrevolutions of the traveling disk, will be approximately the fractionexpressed by the decimal .111-16 multiplied by the number of completerevolutions of each disk. For instance, to find the circumference of acircleI four inches in diameter, it will be seen that in turning thetraveling disk 18, four times, the fractional disk will have made fourrevolutions, and approximately nine-sixteenths of a revolution, ornine-sixteenths of a revolution more than the traveling disk.Ninesixteenths added to three times four, the number of revolutions ofthe traveling disk, equals 12 9/16, or 12.56, which is the circumferenceof a circle of four inches in diameter.

To read the area of a four inch circle, the casing is reversed, so thatthe side containing the chart is brought into view, and it will then befound, assuming the completion of the operation just explained, that theindicator having made a complete circuit or revolution by virtue of itsgea-r connection, is again at the line A and the area of a four inchcircle as 12.56, is found in the space included between the radial linesintersecting the innermost zone, being what I will term the firstsection, or that immediately adjacent and on the right hand side of theradial line A when the instrument is held in the position .shown in Fig.1 and so that the pointer has its exposed extremity uppermost. We lookfor the area of the circle under consideration within the innermostzone, because this is the zone in which the areas of the series ofcircles having diameters beginning with four inches and increasing up toseven and three-fourth inches are found. Again, to find thecircumference and area of a circle whose diameter is fourteen inches, Iturn the traveling disk 18,

fourteen times, when the fractional disk 20 will have made sixteenrevolutions, or two more than the traveling disk. Two added to threetimes fourteen, the number of revolutions of the larger disk, equalsforty-four, which is the circumference of a circle of fourteen inches indiameter. As the true circumference of a circle having a diameter offourteen inches is L13.98, two figures only of the decimal beingexpressed, it will be seen that my improved instrument will come withinone-two hundredth of an inch of a true circumference, which will answer,most purposes where the said dimensions of circles are required.

In the example last above, the indicator 19 will have traveled three andone-half circuits and will rest at the radial line C from which may beread the area of a crcle fourteen inches in diameter, as 153.94 squareinches.

Having thus described my invention, what I claim is,-

1. A computing instrument comprising a casing, two disks mounted torotate thereon, and an operative connection between the two diskswhereby for each revolution of the first disk, the second disk will begiven one revolution and a fraction of a revolution, the said fractionbeing approximately equal to the decimal expression .1416.

2. A computing instrument comprising a casing, a spindle journaled insaid casing, a manipulating disk fast on said spindle, a toothed wheelalso fast on the spindle, a second toothed wheel larger than the firstwheel and meshing therewith, a third toothed wheel smaller than thefirst named wheel and carrying a disk graduated to indicate parts of itscircumference, the arrangement being such that for each revolution ofthe first named disk, the second disk will be given one revolution plusa fraction of a revolution, the said fraction being approximately equalto the decimal expression .1416.

3. A computing instrument comprising a casing, a spindle journaled insaid casing, a manipulating disk fast on said spindle, a toothed wheelalso fast on the spindle, a second toothed wheel larger than the irstnamed wheel and meshing therewith,athird toothed wheel smaller than thefirst named toothed wheel and carrying a disk graduated to indicateparts of its circumference, the arrangement being such that for eachrevolution of the first named disk, the second disk will be given onerevolution and a fraction of a revolution, the said fraction beingapproximately equal to the decimal expression .1416, a spindle uponwhich the said larger gear is mounted and made fast, and a pointer alsoattached to said spindle, whereby a complete revolution of the largergear will impart a corresponding travel to the pointer.

In testimony whereof I aiiix my signature in presence of two witnesses.

JOHN J. WHITE.

Witnesses MAZE KIRBY, A. EBERT OBRLEN.

Copies of this patent may be obtained for ve cents each, by addressingthe Gommissoner of Patents, Washington, D. C.

